Theorems · Definition · ring theory
Algebra.algebraMap
(R : Type u) → (A : Type v) → {inst : CommSemiring R} → {inst_1 : Semiring A} → [self : Algebra R A] → R →+* AEmbedding R →+* A given by Algebra structure.
- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 4,706 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 84 definitions · uses no axioms
- Assumes
- Algebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
Cited by5,099
Results whose statement or proof uses this declaration.
- Algebra.adjoinproof · cited by 535
- minpolyproof · cited by 439
- IsIntegralproof · cited by 427
- IntermediateField.adjoinproof · cited by 382
- MvPolynomial.aevalproof · cited by 298
- Algebra.smul_defstatement · cited by 287
- IsScalarTower.toAlgHomproof · cited by 232
- FaithfulSMul.algebraMap_injectivestatement · cited by 198
- Ideal.underproof · cited by 170
- Algebra.ofIdproof · cited by 166
- Algebra.linearMapproof · cited by 157
- Algebra.algebraMapSubmonoidproof · cited by 137
Showing the 200 most cited of 5,099.